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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Tue, 21 Nov 2006 16:32:37 +0100

Le 21-nov.-06, à 03:42, Tom Caylor a écrit :

*> 1. What is the purpose of this 0-person? What role does it play? As
*

*> soon as we say it has a purpose or role, we've just instantiated it.
*

*> Why do you (or Plotinus) think we need it?
*

The 0-person is the big whole. It is the "everything". A physicalist

could say it is the whole UNIverse. A physicalist MW could say: it is

the whole multiverse. It is something which could only be viewed from

outside the universe: that is from nowhere.

Let me give the arithmetical interpretation of the plotinian hypostases

(person pov). You can consider it as a "toy" plotinian-like (and thus

neoplatonist) theology.To each (lobian) machine we can associate such

an arithmetical interpretation. Then it can be shown that we get the

same logical and mathematical structure for the theology of a large

class of machine (the *sound* lobian one, i.e. the correct or honest

ideal machine which asserts only true sentences (independently of us

knowing that or not: we do classical math).

The eight hypostases:

1) The zero-person pov is the "ONE": I propose to interpret it by

arithmetical truth. By Tarski theorem, the sound lobian machine cannot

even define or name it. Note that the machine can built powerful

approximation of it, but the machine get into inconsistency or

incorrectness once she confuses the ONE and any of its approximations.

2) The third person point of view is the "INTELLECT". I propose to

interpret it by the communicable or provable third person discourse by

the correct machine about herself. The modal logical skeleton (Bp) is

given by the modal logic G. By Solovay theorem it extends naturally

into a richer modal logic G* which proves many more correct, but

unprovable by the machine, propositions. So the intellect, like with

the neoplaonists, splits into two hypostases: the discursive or

"terrestrial" intellect, which is the one described by G, and the

divine one G*. "divine" just means "true", by the arithmetical

interpretation of the "ONE".

3) The first person point of view is the "ALL-SOUL" or "UNIVERSAL SOUL"

described by Plotinus. I define it by the knower, which I define by the

Theaetetical trick, which according to the scholars Brehier is the way

Plotinus proceeds too. So the knowledge modality is defined by Bp & p.

By a kind of mathematical magic, the soul does not split. The "divine"

G* and the "terrestrial" G have the same discourse about its logic. You

can find a proof of this in Boolos 1979 or Boolos 1993. The logic you

get here is known as S4Grz (S4-Grzegorczyk). It is indeed a knower

logic (unlmike G or G*). It is a logic of unnameable self and/or

unnameable time.

4) The first person "plural" point of view, or the Plato-Plotinus'

INTELLIGIBLE MATTER, will be interpreted by Bp & Dp, or equivalently

(cf Kripke semantics of G): Bp & Dt. This leads to the Z logic. By the

Godel completeness theorem this is equivalent with "p is true in all

accessible world & there is at least one world". From the machine

terrestrial point of view, it is not equivalent with Bp, by the

incompleteness theorem. "Dt" (the consistency of "1 = 1" is the same

as the non provability of the false). We have to add "Dt" for having a

notion of probability on the computational continuations (cf UDA).

Unlike the soul S4Grz, G* proves more about Z than G, this gives rise

to Z*.

5) Then the "true first person plural", that is: (Bp & p) & Dt leads to

the sensible feeler or "SENSIBLE MATTER" in the plotinian terminology.

Again the feeler splits into two different logic: which I call X and

X*.

To extract the physical law: you have to add the comp hypothesis. I

will explain later that this can be done by adding "p -> Bp" to the

logic G. This changes all the 8 hypostases. The new logics are written

with their old name + "1". If either S4Grz1 or Z1* or X1* does not

obey quantum logic, then comp is refuted. Until now, evidences exist

that the three logics S4Grz1, Z1*, and X1* do obey at least minimal

form of quantum logic, and this in a sufficiently constructive way that

there is an algorithm for extracting arithmetical interpretation of a

notion of quantization. Of course a lot of works remains to be done:

even the simplest of all Bell inequalities remain untractable when

traduce in those logics. Alas.

*>
*

*> 2. This 0-person cannot be the basis for saying that the scientific
*

*> discourse (and allegedly the Everything List discussions) has to have
*

*> an impersonal basis. As you say, this 0-person has no discourse. And
*

*> the hypothetical existence of a 0-person does not rule out the
*

*> existence of person at the deepest level to which we can relate (as
*

*> persons).
*

The trick is that a lobian machine as rich as ZF is able to prove the

whole (provable and unprovable by PA) theology of a simpler lobian

machine like PA. There is nothing hypothetical in the notion of

"arithmetical truth" from the pov of a rich (set theoretically based)

lobian machine. Faith arrives only when a machine begins to bet on its

*own* correct theology, i.e. its *own* G* if you want (or G* minus G).

*> I believe the reasoning behind an impersonal basis is based
*

*> on the desire to get away from the personal at the core level of being.
*

I don't think so. It comes only from the scientist desire to get away

of first person truth in the scientific discourse. Actually, the cute

thing here is that we get a extremely powerful defense of the existence

of the first person, at the core level of being (despite the need to

restrict the scientific discourse in the third person discourse).

*> What are the steps for logical inference from mathematical consistency
*

*> to the existence of God?
*

I was quoting Benacerraf. No need to accept such definition too

seriously. In particular "consistency of math" or "self-consistency"

are nameable concepts, by the machine. Nothing to do with the unameable

plotinian ONE (here: arithmetical truth for PA, set theoretical truth

for ZF, TomCaylorable truth for Tom Caylor (if I may say)).

*> What are the steps of logical inference from incompleteness to the
*

*> Holocaust?
*

I don't take this too literally. But I have explained, to you and

George if you remember, that the price of being a universal machine is

that you are "crashable". And then the price of being a "sufficiently

rich" universal machine is that not only you are crashable but you

"know" it or "can guess it" (there are some nuances but I simplify). So

the UTM can be frustated somehow. Now frustation of a large collection

of machines could well lead to human catastrophe. I mean I can conceive

this.

Exercice: show that the UD is not a Universal Machine (at all). It is

enough to show that the UD cannot crash. Indeed it has no inputs! (Now

there is a sense in which we could say that the UD is "borned crashed"

given that it is programmed for non stopping (my usual definition of

crashed). So there is a sense to say that the UD is a "crashed

universal machine".

*>
*

*> Weyl quote is interesting though in that it cites the infinite in the
*

*> first half in reference to good, and it cites our finiteness in the
*

*> second half in reference to evil.
*

*>
*

*> I would say that our finiteness (or other limitations such as a need
*

*> for a particular reference frame) is not sufficient for the existence
*

*> of evil.
*

Let me restate more precisely what I say above. Let us interview PA and

ask her if there is a reality. By the godel completeness theorem you

can express this by Dt (= there is an accessible world/model/reality).

As any correct lobian machine, PA will crash on this question. You will

have to reboot it. Or you can talk with the chatty version of PA, which

dovetails on all its proofs (and thus by incompleteness this cannot be

a universal dovetailer for absolute provability). Such a PA will not

crash indeed, but at some point she will assert the second

incompleteness theorem (which *is* provable by the machine: a point

that Penrose did not take enough into account). That is the machine

will assert:

Bf v DBf (we know it by the G theorems, or by PA proves: Beweisbar

('f') or Consistent(Beweisbar ('f') ).

= I will prove some absurdity or it is consistent that I will prove

some absurdity.

This is what I have summed up yesterday by "shit happens or shit may

happen".

This reflects that the machine has enough introspection to prove its

own limitation. In the multiverse which verify (Bf v DBf), a cul-de-sac

world is accessible from each world.

But "Bf" can be fuzzify a lot and play the role of death, madness,

dream, lies, etc... Not so far from some notion of evil.

Yes, evil belongs intrinsically to the realm of the ideally correct

self-observing universal machine.

I hope all people see that "Dt -> ~BDt" and "Bf v DBf" are just two

equivalent versions of Godel's second incompleteness theorem; please

ask if there is a problem here. It would be sad to be stuck here for

reason of having no good base in elementary propositional calculus;

there is no shame to ask question especially for the

non-mathematicians. Here we use the tautological equivalence between (p

-> q) and (~p v q).

*> I agree with your assessment of science. I also believe that science
*

*> does not solve all of our problems.
*

OK. Sure. Provably so with the (a)comp hyp.

[by "deriving something from (a)comp" I mean you can derive it "easily"

from UDA (and thus with the yes doctor) or with AUDA (that is

"arithmetically" and without using the yes doctor. The "a" in (a)comp

is for arithmetical].

*>
*

*>>
*

*>>
*

*>>>
*

*>>> Getting back to the more impersonal question, as has been observed on
*

*>>> this List multiple times, there is a problem with discerning the
*

*>>> source
*

*>>> of order in the universe.
*

*>>
*

*>>
*

*>> In which "universe"? (physical, mathematical, computer-theoretical,
*

*>> arithmetical ...).
*

*>> The word universe is worst than the word "god" in the sense that many
*

*>> people, since about 1500 years, take for granted that there is a
*

*>> primitively physical universe. But such an assumption is no more an
*

*>> explanation than the dishonest use of "God" during centuries.
*

*>>
*

*>>
*

*>
*

*> But is there not a problem with discerning the source of order in
*

*> whatever multiverse that has been hypothesized? I think your point is
*

*> similar to mine, that "natural order" is a relative term, as I see in
*

*> your related posts.
*

Yes. I think so. Precisely: if (a)comp is true the "natural order" is

given by S4Grz1, or Z1(*), or X1(*).

The natural order should emerge from the recollable or glueable

machine's dreams (number relative computation from some internal point

of view).

*>>> Proposed explanations include the use of ideas such as the Anthropic
*

*>>> Principle,
*

*>>> Occam's Razor, some kind of "measure", numbers, local order at
*

*>>> the expense of disorder somewhere else far away, etc. So again, in
*

*>>> the
*

*>>> light of this lack of understanding, it seems pretty presumptuous for
*

*>>> us to say that there must not be interventions in the natural order
*

*>>> simply because we don't see any as we've defined them.
*

*>>
*

*>>
*

*>> I agree with you. But the word "god" and "natural order" are very
*

*>> fuzzy, and rather dangerous to use out of an axiomatic or scientific
*

*>> context, and, as I said, such notion have been out of the realm of
*

*>> ratio since the closure of Plato Academy.
*

*>>
*

*>
*

*> This is my point. We go too far when we let our view of the "natural
*

*> order" (or "god"!) be the dictator of what can happen. Indeed this is
*

*> actually making ourselves the center of the universe (multiverse).
*

*> This is against the true essence of spirituality.
*

I agree with you. "Naturalism" as implicit metaphysics or theology is

as fake as any form of authoritative dogma. Of course a *doubting*

naturalist can remain scientific. But a naturalist who says that when

we die, we will not born again (like many materialist believes) is just

"religious" in the worst sense of the word. The truth is that we don't

know, but can propose theories.

With comp, it is easy to kill oneself ... locally. It is harder ...

globally. With comp it remains possible that consciousness is a sort

of prison, as Otto Rossler extracts from Descartes (I agree with him on

that).

*> If God is the one who does miracles, then from his Gods-eye view a
*

*> miracle is simply a rare event, not inconsistent at all. But from our
*

*> view a miracle is something that punctuates the equilibrium of the
*

*> computable "natural order" that we have deduced from the relative calm
*

*> in which we live.
*

Perhaps. I have only extracted the logic of "probability/credibility

one". I will cautiously not venture myself on the very hard notion of

"historical rare event" (as opposed to the "future" white rabbits,

which must be explained away if the comp idea has to survive).

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Tue Nov 21 2006 - 10:33:41 PST

Date: Tue, 21 Nov 2006 16:32:37 +0100

Le 21-nov.-06, à 03:42, Tom Caylor a écrit :

The 0-person is the big whole. It is the "everything". A physicalist

could say it is the whole UNIverse. A physicalist MW could say: it is

the whole multiverse. It is something which could only be viewed from

outside the universe: that is from nowhere.

Let me give the arithmetical interpretation of the plotinian hypostases

(person pov). You can consider it as a "toy" plotinian-like (and thus

neoplatonist) theology.To each (lobian) machine we can associate such

an arithmetical interpretation. Then it can be shown that we get the

same logical and mathematical structure for the theology of a large

class of machine (the *sound* lobian one, i.e. the correct or honest

ideal machine which asserts only true sentences (independently of us

knowing that or not: we do classical math).

The eight hypostases:

1) The zero-person pov is the "ONE": I propose to interpret it by

arithmetical truth. By Tarski theorem, the sound lobian machine cannot

even define or name it. Note that the machine can built powerful

approximation of it, but the machine get into inconsistency or

incorrectness once she confuses the ONE and any of its approximations.

2) The third person point of view is the "INTELLECT". I propose to

interpret it by the communicable or provable third person discourse by

the correct machine about herself. The modal logical skeleton (Bp) is

given by the modal logic G. By Solovay theorem it extends naturally

into a richer modal logic G* which proves many more correct, but

unprovable by the machine, propositions. So the intellect, like with

the neoplaonists, splits into two hypostases: the discursive or

"terrestrial" intellect, which is the one described by G, and the

divine one G*. "divine" just means "true", by the arithmetical

interpretation of the "ONE".

3) The first person point of view is the "ALL-SOUL" or "UNIVERSAL SOUL"

described by Plotinus. I define it by the knower, which I define by the

Theaetetical trick, which according to the scholars Brehier is the way

Plotinus proceeds too. So the knowledge modality is defined by Bp & p.

By a kind of mathematical magic, the soul does not split. The "divine"

G* and the "terrestrial" G have the same discourse about its logic. You

can find a proof of this in Boolos 1979 or Boolos 1993. The logic you

get here is known as S4Grz (S4-Grzegorczyk). It is indeed a knower

logic (unlmike G or G*). It is a logic of unnameable self and/or

unnameable time.

4) The first person "plural" point of view, or the Plato-Plotinus'

INTELLIGIBLE MATTER, will be interpreted by Bp & Dp, or equivalently

(cf Kripke semantics of G): Bp & Dt. This leads to the Z logic. By the

Godel completeness theorem this is equivalent with "p is true in all

accessible world & there is at least one world". From the machine

terrestrial point of view, it is not equivalent with Bp, by the

incompleteness theorem. "Dt" (the consistency of "1 = 1" is the same

as the non provability of the false). We have to add "Dt" for having a

notion of probability on the computational continuations (cf UDA).

Unlike the soul S4Grz, G* proves more about Z than G, this gives rise

to Z*.

5) Then the "true first person plural", that is: (Bp & p) & Dt leads to

the sensible feeler or "SENSIBLE MATTER" in the plotinian terminology.

Again the feeler splits into two different logic: which I call X and

X*.

To extract the physical law: you have to add the comp hypothesis. I

will explain later that this can be done by adding "p -> Bp" to the

logic G. This changes all the 8 hypostases. The new logics are written

with their old name + "1". If either S4Grz1 or Z1* or X1* does not

obey quantum logic, then comp is refuted. Until now, evidences exist

that the three logics S4Grz1, Z1*, and X1* do obey at least minimal

form of quantum logic, and this in a sufficiently constructive way that

there is an algorithm for extracting arithmetical interpretation of a

notion of quantization. Of course a lot of works remains to be done:

even the simplest of all Bell inequalities remain untractable when

traduce in those logics. Alas.

The trick is that a lobian machine as rich as ZF is able to prove the

whole (provable and unprovable by PA) theology of a simpler lobian

machine like PA. There is nothing hypothetical in the notion of

"arithmetical truth" from the pov of a rich (set theoretically based)

lobian machine. Faith arrives only when a machine begins to bet on its

*own* correct theology, i.e. its *own* G* if you want (or G* minus G).

I don't think so. It comes only from the scientist desire to get away

of first person truth in the scientific discourse. Actually, the cute

thing here is that we get a extremely powerful defense of the existence

of the first person, at the core level of being (despite the need to

restrict the scientific discourse in the third person discourse).

I was quoting Benacerraf. No need to accept such definition too

seriously. In particular "consistency of math" or "self-consistency"

are nameable concepts, by the machine. Nothing to do with the unameable

plotinian ONE (here: arithmetical truth for PA, set theoretical truth

for ZF, TomCaylorable truth for Tom Caylor (if I may say)).

I don't take this too literally. But I have explained, to you and

George if you remember, that the price of being a universal machine is

that you are "crashable". And then the price of being a "sufficiently

rich" universal machine is that not only you are crashable but you

"know" it or "can guess it" (there are some nuances but I simplify). So

the UTM can be frustated somehow. Now frustation of a large collection

of machines could well lead to human catastrophe. I mean I can conceive

this.

Exercice: show that the UD is not a Universal Machine (at all). It is

enough to show that the UD cannot crash. Indeed it has no inputs! (Now

there is a sense in which we could say that the UD is "borned crashed"

given that it is programmed for non stopping (my usual definition of

crashed). So there is a sense to say that the UD is a "crashed

universal machine".

Let me restate more precisely what I say above. Let us interview PA and

ask her if there is a reality. By the godel completeness theorem you

can express this by Dt (= there is an accessible world/model/reality).

As any correct lobian machine, PA will crash on this question. You will

have to reboot it. Or you can talk with the chatty version of PA, which

dovetails on all its proofs (and thus by incompleteness this cannot be

a universal dovetailer for absolute provability). Such a PA will not

crash indeed, but at some point she will assert the second

incompleteness theorem (which *is* provable by the machine: a point

that Penrose did not take enough into account). That is the machine

will assert:

Bf v DBf (we know it by the G theorems, or by PA proves: Beweisbar

('f') or Consistent(Beweisbar ('f') ).

= I will prove some absurdity or it is consistent that I will prove

some absurdity.

This is what I have summed up yesterday by "shit happens or shit may

happen".

This reflects that the machine has enough introspection to prove its

own limitation. In the multiverse which verify (Bf v DBf), a cul-de-sac

world is accessible from each world.

But "Bf" can be fuzzify a lot and play the role of death, madness,

dream, lies, etc... Not so far from some notion of evil.

Yes, evil belongs intrinsically to the realm of the ideally correct

self-observing universal machine.

I hope all people see that "Dt -> ~BDt" and "Bf v DBf" are just two

equivalent versions of Godel's second incompleteness theorem; please

ask if there is a problem here. It would be sad to be stuck here for

reason of having no good base in elementary propositional calculus;

there is no shame to ask question especially for the

non-mathematicians. Here we use the tautological equivalence between (p

-> q) and (~p v q).

OK. Sure. Provably so with the (a)comp hyp.

[by "deriving something from (a)comp" I mean you can derive it "easily"

from UDA (and thus with the yes doctor) or with AUDA (that is

"arithmetically" and without using the yes doctor. The "a" in (a)comp

is for arithmetical].

Yes. I think so. Precisely: if (a)comp is true the "natural order" is

given by S4Grz1, or Z1(*), or X1(*).

The natural order should emerge from the recollable or glueable

machine's dreams (number relative computation from some internal point

of view).

I agree with you. "Naturalism" as implicit metaphysics or theology is

as fake as any form of authoritative dogma. Of course a *doubting*

naturalist can remain scientific. But a naturalist who says that when

we die, we will not born again (like many materialist believes) is just

"religious" in the worst sense of the word. The truth is that we don't

know, but can propose theories.

With comp, it is easy to kill oneself ... locally. It is harder ...

globally. With comp it remains possible that consciousness is a sort

of prison, as Otto Rossler extracts from Descartes (I agree with him on

that).

Perhaps. I have only extracted the logic of "probability/credibility

one". I will cautiously not venture myself on the very hard notion of

"historical rare event" (as opposed to the "future" white rabbits,

which must be explained away if the comp idea has to survive).

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Tue Nov 21 2006 - 10:33:41 PST

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